The use of optical fiber has grown tremendously over the last decades. Optical-fibers are used in numerous applications such as in telecommunications. Telecommunication applications include for example applications in global networks and desktop computers. Such telecommunication applications may involve the transmission of voice, data, or video over distances of less than a meter to thousands of kilometers.
Over the last twenty years, the demand for more network capacity has significantly increased as a result of the development of internet and of the growing traffic generated by an increasing number of internet users. Optical fiber transmissions appear as key technologies to meet such continuous demand for higher transmission data rates in global telecommunication infrastructures. Optical fibers are used as a means to transmit light between two ends in fiber-based communication systems. The light carries data and allows transmission over long distances at higher bandwidths than in wire-based or wireless communication systems.
Optical fibers represent optical waveguides that guide electromagnetic waves in the optical spectrum. The propagation of the waves along an optical fiber depends on several parameters related to the fiber such as its geometry, its mode structure, the distribution of the refractive index, and the material it is made of. Optical fibers typically include a transparent core surrounded by a transparent cladding material with a lower index of refraction. Light carrying data propagates in the fiber, which acts as a waveguide, following a succession of internal reflections.
Optical fibers can be classified into two categories depending on the number of propagation modes (also called “transverse modes”, “spatial modes” or “spatial propagation modes”) which can be supported by the fiber. These modes define the distribution of the waves while propagating in the fiber.
Optical fibers include single-mode fibers (SMF) and multimode fibers (MMF). Single mode fibers are designed to carry light according to a single mode, termed the “fundamental mode”. A single-mode optical fiber cable has a core of a small diameter that allows only the fundamental mode to propagate. As a result, the number of light reflections created as the light passes through the core decreases and leads to low attenuations and fast propagation of the signal. Single mode fibers are typically used for long distances applications.
Multi-mode fibers allow the propagation of many modes in a single-core or multi-core fibers where each core can be single-mode or multi-mode. A multi-mode optical fiber cable has a core of a large diameter that allows the propagation of multiple modes of light. As a result, the number of reflections created as the light passes through the core increases, creating the ability to propagate more data at a given time slot. The various propagation modes form a set of orthogonal channels over which independent data symbols can be multiplexed. Space Division Multiplexing (SDM) techniques and in particular mode division multiplexing (MDM) techniques can be used for this purpose and can enable a multiplication of the capacity of a link by the number of propagating modes.
Multi-mode fibers can offer higher transmission rates than single-mode fibers. However, taking advantage of the presence of multiple modes to multiplex and transmit larger amount of data symbols requires managing several modal detrimental impairments. These impairments are mainly due to imperfections of the optical components (e.g. fibers, amplifiers and multiplexers) and to the crosstalk effects between the various propagation modes. Such imperfections induce non-unitary impairments, i.e. impairments that cause a loss of orthogonality and/or a loss of energy between the different channels over which independent data symbols are multiplexed. Such impairments can significantly reduce the capacity of the optical links and deteriorate the performance of the transmission system, particularly in long distances applications.
In particular, propagating modes through multi-mode fibers are affected by a non-unitary crosstalk known as mode dependent loss (MDL). MDL effects require either optical or digital signal processing solutions to be reduced.
Optical solutions using mode scrambling or strong mode coupling were proposed to reduce the impact of MDL on the capacity of optical fiber links. For example, a technique based on placing mode scramblers between the fiber spans is disclosed in “A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, B. Lankl, Mode Scramblers and Reduced-Search Maximum-Likelihood Detection for Mode-Dependent-Loss-Impaired Transmission, In the Proceedings of the European Conference and Exhibition on Optical Communication, September 2013”. This technique enables the reduction of the MDL effect. However, it fails to completely mitigate MDL and requires a high number of scramblers which induces an additional implementation complexity of the transmission system.
In the presence of N spatial modes, the multi-mode fiber-based transmission system can be modeled as a N×N optical Multiple-Input Multiple-Output (MIMO) system. The optical transmitter sends data symbols over the N modes and the optical receiver receives N different replicas of the original symbols over the N different available modes. Based on this observation, digital signal processing solutions using Space-Time codes were recently investigated in “E. Awwad, G. Rekaya-Ben Othman, Y. Jaouën, and Y. Frignac, Space-Time Codes for Mode-Multiplexed Optical Fiber Transmission Systems, OSA Advanced Photonics Congress: Signal Processing for Photonic Communications (SPPCom), San Diego-USA, July 2014”. The use of existing Space-Time codes such as the Silver code, the Golden code, the TAST (for Threaded Algebraic Space-Time) code, and the Alamouti code for MDL mitigation was analyzed in this article for SDM systems involving 3 and 6 propagation modes. Such analysis highlighted the promising potential of the use of Space-Time codes for MDL mitigation at low implementation costs.
Existing coding solutions use Space-Time codes originally designed for data multiplexing and coding in wireless environments characterized by Rayleigh fading propagation models. Although optical-fiber transmission systems can be represented as MIMO systems, the optical fiber propagation environment differs from the wireless one. Consequently, existing Space-Time codes may not be sufficiently adapted to optical MIMO systems, in particular to SDM systems.
There is accordingly a need for designing digital coding techniques enabling a complete mitigation of MDL effects for SDM systems.